A note on species realizations and nondegeneracy of potentials

2017/03/28 by López-Aguayo, Daniel
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1703.09413

Abstract

In this note we show that a mutation theory of species with potential can be defined so that a certain class of skew-symmetrizable integer matrices have a species realization admitting a non-degenerate potential. This gives a partial affirmative answer to a question raised by Jan Geuenich and Daniel Labardini-Fragoso. We also provide an example of a class of skew-symmetrizable 4 × 4 integer matrices, which are not globally unfoldable nor strongly primitive, and that have a species realization admitting a non-degenerate potential.

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